Chapter 13.2, Problem 44E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the area between the curve y   =   e − x and the x-axis from x =   − 1  to  x   =   1 .

To determine

To calculate: The area between the curve y=ex and the x-axis from x=1 to x=1.

Explanation

Given Information:

The provided curve is y=ex and the range of x-axis is from x=1 to x=1.

Formula used:

The area under a curve from a to b is the absolute value of the definite integral of the function calculated with the lower limit a and upper limit b.

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral exdx=ex.

Calculation:

The provided curve is y=ex and the range of x-axis is from x=1 to x=1.

Thus, the upper limit for x is 1 and the lower limit is 1.

Recall that area under a curve from a to b is the absolute value of the definite integral of the function calculated with the lower limit a and upper limit b.

Thus, the area between the curve and the x-axis is given by the integral 11exdx.

Simplify the integral, use the formula exdx=ex

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